Define cops: More properly, police officers, deputy sheriffs, state traffic officers, state patrols, etc, at commissioned or sworn at the no higher than the state level.
Not cops: Border Patrol, FBI special agents, ATF agents, National Park Rangers, sundry federal protective service agents, Secret Service agents, door shakers, renta-cops, etc.
The difference: Powers to make arrests without warrants based upon probable cause.
The feds have to get a warrant to arrest a citizen unless they act as private persons with the same limitations upon them. Why: They're NOT COPS
EXCEPTION: On federal property, ie, National Parks, Indian reservations, federal property such as the White House, federal buildings, military reservations, etc. If you were to base your understanding on TV you might get another impression because they are protrayed as having Probable Cause arrest powers.